If `veca,vecb and vecc` are non coplanar and unit vectors such that `vecaxx(vecbxxvecc)=(vecb+vecc)/sqrt2)` then the angle between `vea and vecb` is (A) `(3pi)/4` (B) `pi/4` (C) `pi/2` (D) `pi`

Options

A. `pi/4`
B. `pi/2`
C. `(3pi)/(4)`
D. `pi`

Answer

C

Explanation

`veca xx (vecb xx vecc) =(overset(-)(b)+overset(-)(c))/(sqrt2) rArr overset(-)(a).overset(-)(c))overset(-)(b)-(overset(-)(a) overset(-)(b))overset(-)(c)=(overset(-)(b)+overset(-)(c))/(sqrt2)`
`rArr [(overset(-)(a).overset(-)(c)-1/sqrt2]overset(-)(b)-[(overset(-)(a).overset(-)(b))+1/sqrt2]overset(-)(c)=0`
`rArr |veca||vecc| cos theta=1/sqrt2, |veca||vecb| cos phi=-1/sqrt2`
`rArr cos theta=1/sqrt2, cos phi=-1/sqrt2 rArr theta=pi/4, phi=(3pi)/(4)`